Spherical stellar systems with spheroidal velocity distributions

Families of anisotropic distribution functions that are consistent with any spherically symmetric density profile are derived by means of a method employing an algorithm which is sufficiently straightforward for the derivation of analytic solutions. Each solution is defined by a single, free, 'anisotropy radius' parameter. The models are isotropic in the center, and become either radially or tangentially anisotropic at large radii. The superposition of two or more solutions with different anisotropies yields models exhibiting any desired velocity structure. Families of line-of-sight velocity dispersion profiles are obtained when the algorithm is applied to a model galaxy with a de Vaucouleurs density law. The algorithm generates physically acceptable solutions with less computational effort than the general linear programming method.